Nta

Ntawm no yog cov qauv thiab cov kev tswj, uas yuav siv tau rau functions.

Ib qho tseem ceeb!! GeoGebra distinguishes nruab nrab ntawm zauv ua ob tog sib luag thiab functions. Yog tias koj xav tau siv cov lus txib sib txawv ntawm cov haujlwm, ces koj rau hauv lub tswv yim dab tsi hom xwb ib feem ntawm qhov kev tswj, uas yog tom qab lub vaj huam sib luag kos npe. Sau ntawv 2x + 3, txawm tias muaj y = 2x + 3.

Thawj Qib Function

Cov kev tswj

Cov kev tswj rau thawj degree Function (ib tug ncaj kab)

\(f(x)\) = \(a\) • x + \(b\)

Qhov muaj nqis \(a\) hu ua txoj kab nqes los yog txob kab nce caug xyoo. Værdien i stedet for \(a\) hais tias ib yam dab tsi txog, ntau npaum li cas tus kab nce los yog ntog. Yog hais tias \(a\) nws zoo, thiaj li yog lub bar nce. Yog hais tias \(a\) nws yog ib qhov tsis zoo, thiaj li yog lub bar Txo.

Qhov muaj nqis \(b\) hais tias, qhov twg txoj kab sib tshuam y-axis (qhov feem ntsug).

FX ces graph tus kab f(x) = 2x + 3 yuav kos los ntawm 3 ntawm y-axis (Ie. dhau ntawm qhov taw tes (0,3) ) thiab nce (txoj kab nqes) nrog 2.

Cov cim qhia

Piv txwv li, mus rau kos npe rau GeoGebra, koj yuav tsum nyob rau hauv lub tswv yim dab tsi sau ntawv

2x + 3

Ntsujplig Theem Function

Cov kev tswj

Cov kev tswj rau ib ntsuj plig theem Function (nyob rau hauv parabel)

\(f(x)\) = \(a\) • x\(^2) + \(b\) • x + \(c\)

Keeb kwm thiab siab tshaj

Koj yuav nrhiav tau tej yam keeb kwm(Pas nrig) (kev sib tshuam cov ntsiab lus nrog x-axis) thiab qhov siab tshaj (heev) siv. ua raws li cov lus txib hauv qhov chaw nkag

Pas nrig[f]
Extremum[f]

Cov cim qhia

Piv txwv li, yog hais tias koj xav kom kos npe rau Function \(f(x)\) = 2 x\(^2) + 3 x – 4 , es koj thiaj li yuav tsum tau ntaus cov nram qab no rau hauv lub tswv yim dab tsi

2*x ^ 2 + 3*x - 4

Diskriminanten

Discriminant hais tias ib yam dab tsi txog, tus naj npawb ntawm cov keeb kwm(kev sib tshuam cov ntsiab lus nrog x-axis) graph muaj. Discriminant suav tawm uas yog siv. ib formal, tias Hedda

D = \(b^2\) – 4 • \(a\) • \(c\)

1. Yog hais tias D < 0 (tsawg tshaj li 0) skærer parablens ‘ben’ TSIS X-lus (TSIS MUAJ daws LUB EQUATION)
2. Yog hais tias D = 0 (vaj huam sib luag rau 0) skærer parablens ‘ben’ X-lus IB qhov chaw. (Daws x =-b /(2ib))
3. Yog hais tias D > 0 (ntau tshaj 0) skærer parablens ‘ben’ X-lus YUAV chaw.

Lub daws s₁ = (-b √ D)/(2ib) og S₂ = (-b-√ D)/(2ib)

Info om ib-, b- thiab c-txiaj

Hauv qab no yog ib tug me ntsis info txog, dab tsi yog ib tug, b thiab c txiaj hais txog graph ntawm Function.

ib tug yog txoj kab nqes ntawm

1. Hvis a er negativ vender parablens ‘ben’ nedad. (sur Smiley)
2. Hvis a er positiv vender parablens ‘ben’ opad. (zoo siab smiley)
3. Qhov ntau dua ib tug, desto smallers parabel
4. Tus me ib, desto Bredero parabel

b hais tias ib yam dab tsi txog, qhov twg parabola lies txheeb ze rau y-axis.

1. Yog hais tias b = 0, Tom qab ntawd lub vertex ntawm parabola nyob ntawm y-axis.
2. Yog hais tias ib tug thiab b muaj tib lub kos npe, ces lub vertex yog rau sab laug ntawm y-axis.
3. Yog hais tias ib tug thiab b muaj cov cim qhia txawv, ces lub vertex yog rau sab xis ntawm y-axis.

c yog lub ntsiab lus ntawm kev sib tshuam ntawm parabola nrog y-axis.

1. Yog hais tias c = 0, ces tus parabola hla dhau qhov taw tes (0,0)